Tag Archives: Morton

We’ve recently been doing some work in PolyVox to switch the ordering of voxel data from linear order to Morton order. This work is now complete, and in this relatively technical post I’m going to highlight a couple of the interesting tricks which we came across while doing it. Hopefully these will be beneficial to other people working on the low-level details of voxel engines.

Like many voxel engines, PolyVox allows volume data to be broken down into a number of ‘chunks’. The primary advantage of this approach is that not all the data has to be loaded into memory at the same time, and we can instead load and unload chunks on demand. Note that this is an implementation detail of the our ‘PagedVolume’ class, and algorithms which operate on the data (mesh extractors, raycasting, etc) are not aware that the data is stored in this way.

The size of each chunk can be specified by the user (with the ideal size depending on a number of factors) but typically contain 32³, 64³, or 128³ voxels. The ‘ordering’ of these voxels refers to the way they are laid out in memory, and two possibilities are shown below for the 2D case. The linear ordering is the easiest to understand and can be traversed with a simple nested for loop, but the Morton ordering brings numerous benefits in terms of locality of reference, ease of downsampling, and increased compressibility.

Linear ordering (left) vs. Morton ordering (right)

However, the purpose of this blog post is not to explain the benefits of Morton ordering, nor to describe how (x,y,z) positions are mapped to locations on the Morton curve. For this we refer you to the Wikipedia article and the excellent blog posts by Jeroen Baert and Fabian Giesen. Instead, we wish to highlight a couple of optimizations which were useful in our implementation.